Abughaush, who was seeded 10th and considered an outsider for a medal in Rio, used his quick footwork and effective kicks to score a 10-6 upset win over the 2012 London Games bronze medallist.
"It's an indescribable feeling to win the first medal in the history of Jordan in all the sports," said Abughaush, who was knocked out in the second round of the world championships last year.
"It's also a great feeling to listen to the national anthem of Jordan being played in Rio in front of the whole world."
Jordan first competed at the Olympics in 1980 in Moscow. The Middle Eastern country of more than seven million people has never sent more than 10 athletes to compete at a Games, with only eight in Brazil.
Abughaush produced a series of upsets to make the final, taking out twice world champion Lee Dae-hoon in the quarter-finals and then gold medal holder Joel Gonzalez in the last four.
Victory drew wild celebrations from the Jordanian delegation at Carioca Arena 3, with Abughaush, who is studying business management, delaying his post-bout news conference to take a call from the Prince of Jordan.
"He said 'congratulations'. He said he was very happy and he was telling me about how all of the people of Jordan are very happy and are even shedding tears of happiness for me," Abughaush said of the conversation.
(Writing by Patrick Johnston in Singapore; editing by Amlan Chakraborty)
